Certification Problem

Input (TPDB TRS_Standard/SK90/2.37)

The rewrite relation of the following TRS is considered.

and(not(not(x)),y,not(z))

→

and(y,band(x,z),x)

(1)

Property / Task

Prove or disprove termination.

Answer / Result

Yes.

Proof (by NaTT @ termCOMP 2023)

1 Dependency Pair Transformation

The following set of initial dependency pairs has been identified.

and^#(not(not(x)),y,not(z))

→

and^#(y,band(x,z),x)

(2)

1.1 Dependency Graph Processor

The dependency pairs are split into 1 component.

The 1^st component contains the pair
and^#(not(not(x)),y,not(z)) → and^#(y,band(x,z),x) (2)

1.1.1 Reduction Pair Processor with Usable Rules
Using the Max-polynomial interpretation

[and(x₁, x₂, x₃)] = 0

[band(x₁, x₂)] = 1

[and^#(x₁, x₂, x₃)] = x₁ + x₂ + 0

[not(x₁)] = 2

having no usable rules (w.r.t. the implicit argument filter of the reduction pair), the pair
and^#(not(not(x)),y,not(z)) → and^#(y,band(x,z),x) (2)
could be deleted.
1.1.1.1 Dependency Graph Processor

The dependency pairs are split into 0 components.